Patch-based Hybrid Modelling of Spatially Distributed Systems by Using Stochastic HYPE - ZebraNet as an Example

Individual-based hybrid modelling of spatially distributed systems is usually expensive. Here, we consider a hybrid system in which mobile agents spread over the space and interact with each other when in close proximity. An individual-based model for this system needs to capture the spatial attributes of every agent and monitor the interaction between each pair of them. As a result, the cost of simulating this model grows exponentially as the number of agents increases. For this reason, a patch-based model with more abstraction but better scalability is advantageous. In a patch-based model, instead of representing each agent separately, we model the agents in a patch as an aggregation. This property significantly enhances the scalability of the model. In this paper, we convert an individual-based model for a spatially distributed network system for wild-life monitoring, ZebraNet, to a patch-based stochastic HYPE model with accurate performance evaluation. We show the ease and expressiveness of stochastic HYPE for patch-based modelling of hybrid systems. Moreover, a mean-field analytical model is proposed as the fluid flow approximation of the stochastic HYPE model, which can be used to investigate the average behaviour of the modelled system over an infinite number of simulation runs of the stochastic HYPE model.Comment: In Proceedings QAPL 2014, arXiv:1406.156

Derivative Formula and Applications for Degenerate Diffusion Semigroups

By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As applications, explicit gradient estimates and Harnack inequalities are derived.Comment: 18 page